Maternal postnatal depressive symptoms and offspring emotional and behavioural development at age 7 years in a UK-birth cohort: the role of paternal involvement

There is considerable variability in developmental outcomes of children whose mothers experience depression. Few longitudinal studies have examined contributions of paternal involvement in the association between maternal postnatal depression (PND) and offspring development. We examined pathways from maternal PND at 8 weeks (Edinburgh Postnatal Depression Scale; total score) to offspring emotional and behavioural development at 7 years (Strengths and Difficulties Questionnaire; total score) through behavioural, affective and cognitive dimensions of paternal involvement in a UK-based birth cohort (Avon Longitudinal Study of Parents and Children; n=3,434). Analyses were adjusted for baseline confounders and paternal postnatal depression (PND; Edinburgh Postnatal Depression Scale; total score) as an intermediate confounder. Maternal PND was strongly associated with offspring development, but this association was not mediated by the combination of all indirect pathways through various dimensions of paternal involvement. Only father-child conflict emerged as a risk factor for adverse offspring development and as a mediator in the association between maternal PND and offspring development (albeit the effect size was small). If found causal, interventions that reduce father-child conflict may reduce the risk of adverse development in offspring of mothers with PND.

months, 2 years 9 months, 3 years 11 months).Extracted items captured various dimensions of paternal involvement, which were initially double-rated and independently assigned into theoretical dimensions by three researchers (IC, RP and TC).This iterative process was followed by larger research group discussions with significant input from experts in early child development and parenting (AS and MB).Individual items fell into two theoretically distinct sources of paternal involvement: (1) child-focused paternal involvement capturing behavioural, affective and cognitive dimensions directed at the child; and (2) motherinfluenced paternal involvement with the child through the lens of maternal expectations, mother-father relationship and indirect material care through support of the mother.The mother-influenced dimensions of paternal involvement acknowledge those aspects that are done for the child but do not entail interactions with the child, as well as the impact of interparental relationship on parent-child relationship (Cabrera et al., 2014;Pleck, 2012).It has been argued that men's engagement and interactions with their children need to be understood through the lens of maternal influences (Marsiglio et al., 2000;Palkovitz, 2019).
Arguablyfathers are more involved when their female partners have supportive attitudes regarding paternal involvement, and less involved when inter-parental relationship is characterised by underlying conflict, marital dissatisfaction and maternal 'gatekeeping' (maternal beliefs and practices that discourage or facilitate paternal involvement; Feldman, 2000;Miller, 2018).Evidence suggests that such influences may be more pronounced for paternal rather maternal involvement and parenting behaviours (Belsky et al., 1991;Schacht et al., 2009).Supporting the mother through sharing household tasks and responsibilities is another important dimension of paternal mother-influenced involvement (Cabrera et al., 2014).It may not directly land itself into an aspect of involvement, however, variations in this behaviour may have important implications for the child (Feldman, 2000;Pleck, 2012).The final factors capturing child-focused paternal involvement (Table S1) encompassed: behavioural (e.g., direct involvement in caregiving), affective (e.g., quality of father-child relationship, such as enjoyment and warmth, conflictual relationship with and worries about the child), and cognitive (e.g., paternal parenting confidence and beliefs regarding caregiving) dimensions.The final factors capturing mother-influenced paternal involvement (Table S2) included: paternal perceptions of maternal beliefs or practices that discourage or facilitate his involvement in childcare (e.g., maternal 'gatekeeping'), paternal help with household tasks and responsibilities (e.g., preparing meals and cleaning home), paternal beliefs regarding mother-father relationship and its impact on parenting (e.g., partner feels hurt by attention mother gives child) and maternal expectations around employment and parenthood (e.g., mother expects partner to take child after work).

Potential Baseline Confounders: Child Polygenic Score for Neuroticism, Socioeconomic, Parental and Family Characteristics
Analyses were adjusted for child polygenic score (PGS) for neuroticism.Genotyped data were available for 8,237 children in the ALSPAC cohort.Previously, 116 independent variants robustly associated with neuroticism have been identified (Luciano et al., 2018).Of these original variants, 109 were available in the ALSPAC participants with the genetic data.
Neuroticism PGS scores were calculated as the sum of the number of copies of each effect allele carried by an individual (ranging from 0 to 2 for each SNP), multiplied by the effect estimate identified in the original GWAS.These weighted standardised neuroticism PGS sum scores were included in the analyses.

Potential Intermediate Confounder: Paternal Postnatal Depression
Analyses were adjusted for paternal postnatal depression (PND) as a potential exposure induced intermediate confounder of the mediator-outcome association (Cole & Hernán, 2002;Sheikh et al., 2016).Paternal PND (self-reported depressive symptoms, no a clinical diagnosis) was assessed using the Edinburgh Postnatal Depression Scale (EPDS; Cox et al., 1987) administered to fathers at 8 months postnatally.The EPDS is a 10-item selfreported depression questionnaire, validated and used extensively to screen for depression during the perinatal period in women and men (Massoudi et al., 2013;Matthey et al., 2001).
Individual items were summed-up to derive a continuous measure (score range 0-24, with higher scores indicating more severe depressive symptoms) to capture the full variation in depressive symptoms.

Latent Factor Models
Individual parenting items were loaded onto the hypothesised parenting dimensions and modelled using Confirmatory Factor Analyses (CFA).To identify the model, the mean of the latent factors was fixed to '0' and their variance to '1'.The majority of individual items loaded strongly onto the factors that they were initially theoretically assigned to.However, some items were moved between the factors if modification indices from the initial model indicated that items would be a better fit on the alternative factor, and this made theoretical sense following discussions by the research group.Additional correlations between similar items that were collected at different time points were added into the models to account for shared variance related to time and the repeated nature of the questions.Derived factors, items and factor loadings for each of the measurement models (child-focused and motherinfluenced paternal involvement) are presented in Tables S1-S2.(Muthén & Muthén, 2015) to estimate direct, total indirect and specific indirect effects with a WLSMV estimator to model continuous and categorical variables.

Missing Data: Multiple Imputation
We imputed missing data due to loss to follow-up because ignoring those with missing data may result in bias by assuming that data are Missing Completely at Random (MCAR; Sterne et al., 2009).We repeated direct and mediated effects analyses on the imputed datasets to account for the loss to follow-up.We used Multivariable Imputation by Chained Equations (MICE; Royston & White, 2011) to impute missing data in exposure, outcome and confounders (except child neuroticism PGS; n=6,029) using the ice command in Stata v.15.1/MP (Stata.Corp., Texas, USA).We did not impute child neuroticism PGS from the phenotype data due to restrictions associated with quality control and participant consent.
ALSPAC provides a wealth of rich, prospectively collected data on a range of sociodemographic, mental health and developmental variables, which enabled us to account for missing data in exposure, outcome and confounders, as well as factors that explain missingness, validating the Missing-At-Random assumption (MAR; White et al., 2011).However, the decision was taken not to impute mediators (child-focused and motherinfluenced dimensions of paternal involvement) as there are no sufficient auxiliary data on fathers' parenting in the ALSPAC cohort to justify the plausibility of MAR assumption.The imputation model was fully compatible with the main analyses.Using binary, ordinal logistic and linear regression models as appropriate, 50 imputed datasets by 10 cycles of regression switching were generated.Monte-Carlo errors were less than 10% of the standard error and FMI values were no larger than 0.5, suggesting that 50 imputed datasets were sufficient (White et al., 2011).Each imputation model contained all variables in the substantive analyses along with over 40 auxiliary variables pertaining to maternal and paternal characteristics (e.g., paternal age) and psychopathology, offspring development and mental health, as well maternal and paternal indices of socioeconomic adversity.MICE imputations were carried out in Stata v.15.1/MP (Stata.Corp., Texas, USA).The imputed datasets were exported into Mplus v.8.3 (Muthén & Muthén, 2015) to estimate direct and indirect (mediated) pathways using MODEL CONSTRAINT command.

Paternal Involvement Factors
Full details of six factors capturing child-focused and four factors capturing motherinfluenced aspects of paternal involvement are provided below.

Child-Focused Paternal Involvement
Factor 1 Paternal parenting confidence: 11 items relating to paternal feelings of confidence in the parenting role and perceptions of the ability to engage effectively in parenting behaviours (e.g., 'partner feels confident with child', 'partner unsure if doing the right thing', 'partner happy with the way he brings up child') were extracted from paternal self-reported questionnaires administered at 8 weeks, 8 months, 1 year 9 months and 2 years 9 months.
Higher factor scores represented higher levels of paternal parenting confidence.
Factor 2 Paternal conflictual relationship with child: 19 items relating to conflict, harsh disciplining and irritation with the child (e.g., 'child gets on partner's nerves', 'partner dislikes mess surrounding child', 'smacking is the best way to discipline child') were extracted from paternal self-reported questionnaires administered at 8 weeks, 8 months, 1 year 9 months and 2 years 9 months.Higher factor scores signified lower levels of conflictual parent-child relationship, irritation with the child and less harshness in paternal disciplining.

MATERNAL POSTNATAL DEPRESSIVE SYMPTOMS AND OFFSPRING DEVELOPMENT: ROLE OF PATERNAL INVOLVEMENT
Factor 3 Paternal enjoyment and warmth: 27 items relating to feelings of enjoyment, affection, love and warmth toward the child (e.g., 'partner enjoys child', 'partner feels very close to child', 'child gives great joy') were extracted from paternal self-reported questionnaires administered at 8 weeks, 8 months, 1 year 9 months, 2 years 9 months and 3 years 11 months.Higher factor scores represented more paternal enjoyment, affection and warmth toward the child.
Factor 4 Paternal involvement in childcare: 8 items describing frequency of paternal involvement in various aspects of childcare (e.g., 'frequency partner feeds child per week', 'frequency partner puts child to bed per week', 'frequency partner bathes child per week') were extracted from paternal self-reported questionnaires administered at 8 weeks and 8 months.Higher factor scores represented higher frequency of paternal involvement in childcare.
Factor 5 Paternal worries about child: 4 items pertaining to paternal worries about the child (e.g., 'partner worries about child when at work', 'partner anxious if someone else looks after child', 'partner worries about study child when at work') were extracted from paternal selfreported questionnaires administered at 1 year 9 months and 2 years 9 months.Higher factor scores represented lower levels of paternal worries about the child.
Factor 6 Paternal beliefs regarding caregiving: 6 items relating to paternal parenting principles and practices related to structure, regularity and routine in infant care (e.g., 'babies should fit into parents' routine', 'babies should be fed when hungry') and attunement, i.e. responsiveness to infant cues (e.g., 'babies should be picked up when cry') were extracted from paternal self-reported questionnaires administered at 8 months and 1 year 9 months.
Higher factor scores represented more paternal appreciation of regular routine and higher levels of attunement and responsiveness to child's cues.

Mother-Focused Paternal Involvement
Factor 1 Paternal help with household tasks: 12 items related to various aspects of paternal help with household tasks (e.g., 'partner helped with cleaning home since birth', 'partner helped with housework since birth', 'partner gave help with preparing meals') were extracted from paternal self-reported questionnaires administered at 8 weeks and 8 months.Higher factor scores represented higher levels of paternal help with household tasks since the child was born.
Factor 2 Paternal perception of maternal 'gatekeeping': 7 items relating to paternal perceptions of maternal beliefs and behaviours that encourage or hinder paternal involvement in childcare, i.e., maternal 'gatekeeping', (e.g., 'mother excludes partner from childcare', 'partner always getting under mother's feet, 'mother dislikes partner being involved with childcare') were extracted from paternal self-reported questionnaires administered at 8 weeks.Higher factor scores indicated higher levels of paternal perception of being supported by the mother and included in childcare, i.e. less maternal 'gatekeeping'.S3).Conflictual father-child relationship was associated with less enjoyment and warmth, less involvement in childcare, less appreciation of structure and more worries about the child.Paternal enjoyment and warmth were associated with more involvement in childcare, more paternal appreciation of structure and higher levels of attunement to child's cues.Paternal worries about the child were associated with less appreciation of structure and less involvement in childcare.Paternal beliefs more concordant with the positive impact of having a child on mother-father relationship were associated with higher levels of paternal help with household tasks and less pressure to manage childcare and employment.Paternal perception of maternal support and inclusion in childcare were associated with higher levels of paternal involvement in household tasks, better ability to manage employment and childcare, and more positive feelings on the changing nature of mother-father relationship following the birth of the child.

Sensitivity Analyses: Missing Data
We repeated direct and mediated effects analyses on imputed datasets to examine the impact of response attrition on our findings.Characteristics of the sample by the completeness of the data are presented in Table S4.Participants comprising our analytical sample were from a higher socioeconomic background as indexed by lower proportion of those reporting financial difficulties and higher proportion of those reporting residing owned/mortgaged accommodation and married marital status compared to the original ALSPAC sample.The results from the analyses using the imputed data supported our findings resulting in the similar pattern of results and over-arching conclusions as our main findings in the complete case analyses (Table S5) with one notable difference.In Model 2, there was stronger evidence for the specific indirect effect through paternal conflictual relationship with the child (β=0.042,95%CIs: 0.005, 0.079, p=0.028), with some emerging evidence for a specific indirect effect through paternal worries about the child although the

First
, we estimated the unadjusted models composed of exposure, outcome and mediators only.Second, we estimated models adjusted for child PGS and all antenatal baseline confounders (Model 1), and further adjusted for paternal PND (8 months) as a possible intermediate confounder of the mediator-outcome association (Model 2), which is also a mediator of the exposure -> mediator association.Thus, our path-specific effects of interest were: (i) Model 1: the indirect effect composed of maternal PND -> paternal involvement -> offspring emotional and behavioural development pathways, and the direct effect, which is the pathway from maternal PND to offspring emotional and behavioural development; (ii) Model 2: the indirect effect composed of a combination of pathways maternal PND -> paternal PND-> paternal involvement -> offspring emotional and behavioural development and maternal PND -> paternal involvement -> offspring emotional and behavioural development pathways, and the direct effect, which is a combination of maternal PND -> paternal PND -> offspring emotional and behavioural development pathways and maternal PND -> offspring emotional and behavioural development pathway.

Figure
Figure 4a-b represent pathways that constitute total indirect (bold lines) and direct (dashed

Factor 3
Paternal beliefs regarding mother-father relationship and parenting: 3 items relating to paternal beliefs regarding the impact of having a child on father-mother relationship (e.g., 'parenthood has made partner and mother closer', 'mother no longer gives partner attention') were extracted from paternal self-reported questionnaires administered at 8 weeks.Higher factor scores represented paternal beliefs more concordant with positive changes in the nature of mother-father relationship following the birth of the child.

Factor 4
Paternal attitudes to employment and parenthood: 5 items relating to paternal beliefs regarding maternal expectations around employment, childcare and paternal difficulties to manage childcare and employment (e.g., 'mother expects partner to take child MATERNAL POSTNATAL DEPRESSIVE SYMPTOMS AND OFFSPRING DEVELOPMENT: ROLE OF PATERNAL INVOLVEMENT after work', 'partner too tired to take child after work', 'partner finds it hard to cope with child after work') were extracted from paternal self-reported questionnaires at 8 weeks and 2 years 9 months.Higher factor scores indicated paternal beliefs concordant with less maternal pressure to look after child after work and less difficulties with managing childcare and employment.Associations Between Child-Focused and Mother-Influenced Dimensions of Paternal Involvement Paternal parenting confidence was strongly associated with less conflictual fatherchild relationship, more paternal enjoyment and involvement in childcare and less paternal worries about the child (Table Maternal PND, Child-Focused and Mother-Influenced Dimensions of Paternal Involvement and Offspring Emotional and Behavioural Development MATERNAL POSTNATAL DEPRESSIVE SYMPTOMS AND OFFSPRING DEVELOPMENT: ROLE OF PATERNAL INVOLVEMENT Full description of estimates for Model 1 is provided below, with full description of estimates for Model 2 provided in the main manuscript.

a
Core ALSPAC sample: no exposure or outcome data; b Complete sample: exposure, outcomes and confounders data available; c Imputed sample: imputed missing data on exposure, outcomes and confounders (except child PGS).PGS: polygenic score for neuroticism; Paternal PND: paternal postnatal depression.

Table S1 .
Derived factors, items, standardised factor loadings and fit indices for the measurement model capturing child-focused dimensions of paternal involvement

Table S2 .
Derived factors, items, standardised factor loadings and fit indices for the measurement model capturing mother-influenced dimensions of paternal involvement

Table S3 .
Associations between child-focused and mother-influenced dimensions of paternal involvement

Table S4 .
Distribution of sociodemographic characteristics in the original Avon Longitudinal Study of Parents and Children (ALSPAC) Cohort and the study complete and

Table S5 .
Estimates of direct and mediated effects in the unadjusted model and models adjusted for child PGS, gender, antenatal baseline confounders, and paternal PND as an intermediate confounder in imputed sample (n=6,029) Note: 1 Effect size are unadjusted and adjusted regression coefficients (B unstandardised); unadjusted model (exposure, outcome and mediators only); Model 1: adjusted for child PGS and antenatal baseline confounders (child gender, financial problems, homeownership status, maternal age and education, parental conflict, marital status); Model 2: further adjusted for paternal PND at 8 months as an intermediate confounder.